Robust Adaptive Fuzzy Control For A Class Of Nonilinear Systems

Since forties of last century, control theory has experience from classical control theory to modern control theory. Now automatic control technologies have been widely used in industry, agriculture, traffic, aviation, aerospace and so on , which have raised working efficiency and improved labor condition.But whether classical control theory or modern control theory need to know the mathematical model of the controlled plant. While most of the controlled plants, strictly, are nonlinear in the real world. It's hard to obtain their mathematical models exactly by traditional method.Fuzzy control technology, which developed from last sixties and seventies, finds broad application in practice for its needing no models and its capability of utilizing specialists' experience and knowledge. Lately, it's found that fuzzy control is a nonlinear control tactics in essence and fuzzy logic systems are universal function approximators. These study results support the application of fuzzy control to nonlinear systems in theory. Recently there has been a surge interest in the fuzzy control of nonlinear systems from the angle of function approximation.But the construction of fuzzy control tactic or fuzzy logic systems is depended on specialists' experience and knowledge too much, which results in the lack of adaptive and learning capabilities and the necessary theory analyses. For these problems there is a better scheme in the field of adaptive fuzzy control of nonlinear systems: firstly a original model of the fuzzy controller or the fuzzy logic system is constructed in accordance with the specialists' knowledge; then a approximation error is defined in the angle of function approximation; after that, based on the approximation error and the control error, an adaptive fuzzy controller or a fuzzy logic system is obtained by Lyapunov design method; finally the control property of the whole closed-loop system, such as the control precision or stability is analyzed. These method is called Lyapunov synthesize method.In this paper, by using the above Lyapunov synthesize method, two robust adaptive fuzzy controllers, one is for state feedback and the other is for output feedback, are designed for the tracking problem of a class of single input and single output unknown nonlinear system. A kind of fuzzy logic system is used to approximate the unknown nonlinearities. Unlike the previous research, this paper considers the existence of the approximation error and the system's external disturbance. Provide the approximation error and the system's external disturbance has an unknown boundary?an adaptive estimation boundary is designed. The final controller guarantees that the closed-loop system is robust stable and tracking error converges to a neighborhood of zero. In the design process of the output feedback controller, a high-gain observation is applied to make the performance of the output feedback controller achieves that of the state feedback controller.